Related papers: Finding the optimal nets for self-folding Kirigami
Designing a robot or structure that can fold itself into a target shape is a process that involves challenges originated from multiple sources. For example, the designer of rigid self-folding robots must consider foldability from geometric…
A long-standing challenge is designing multi-scale structures with good connectivity between cells while optimizing each cell to reach close to the theoretical performance limit. We propose a new method for direct multi-scale topology…
Rigidly and flat-foldable quadrilateral mesh origami is the class of quadrilateral mesh crease patterns with one fundamental property: the patterns can be folded from flat to fully-folded flat by a continuous one-parameter family of…
Four rigid panels connected by hinges that meet at a point form a 4-vertex, the fundamental building block of origami metamaterials. Here we show how the geometry of 4-vertices, given by the sector angles of each plate, affects their…
We study the problem of maximizing the number of full degree vertices in a spanning tree $T$ of a graph $G$; that is, the number of vertices whose degree in $T$ equals its degree in $G$. In cubic graphs, this problem is equivalent to…
We study dynamic planar graphs with $n$ vertices, subject to edge deletion, edge contraction, edge insertion across a face, and the splitting of a vertex in specified corners. We dynamically maintain a combinatorial embedding of such a…
In this paper we consider the problem of connected edge searching of weighted trees. It is shown that there exists a polynomial-time algorithm for finding optimal connected search strategy for bounded degree trees with arbitrary weights on…
An independent edge set of graph $G$ is a matching, and is maximal if it is not a proper subset of any other matching of $G$. The number of all the maximal matchings of $G$ is denoted by $\Psi(G)$. In this paper, an algorithm to count…
The paper deals with optimality issues in connection with updating beliefs in networks. We address two processes: triangulation and construction of junction trees. In the first part, we give a simple algorithm for constructing an optimal…
Kirigami is the art of cutting paper to make it articulated and deployable, allowing for it to be shaped into complex two and three-dimensional geometries. The mechanical response of a kirigami sheet when it is pulled at its ends is enabled…
Origami, the traditional art of paper folding, has revolutionized science and technology in recent years and has been found useful in various real-world applications. In particular, origami-inspired structures have been utilized for…
We study a recent model of random networks based on the presence of an intrinsic character of the vertices called fitness. The vertices fitnesses are drawn from a given probability distribution density. The edges between pair of vertices…
The ancient art of origami, traditionally used to transform simple sheets into intricate objects, also holds potential for diverse engineering applications, such as shape morphing and robotics. In this study, we demonstrate that one of the…
We show that a network can self-organize its structure in a completely distributed manner in order to optimize its synchronizability whilst satisfying the local constraints: non-negativity of edge weights, and maximum weighted degree of…
The brain's connectome and the vascular system are examples of physical networks whose tangible nature influences their structure, layout, and ultimately their function. The material resources required to build and maintain these networks…
We present a direct method for solving the inverse problem of designing isotropic potentials that cause self-assembly into target lattices. Each potential is constructed by matching its energy spectrum to the reciprocal representation of…
We consider the problem of constructing an an optimal-weight tree from the 3*(n choose 4) weighted quartet topologies on n objects, where optimality means that the summed weight of the embedded quartet topologiesis optimal (so it can be the…
Flat origami studies straight line, planar graphs $C=(V,E)$ drawn on a region $R\subset\mathbb{R}^2$ that can act as crease patterns to map, or fold, $R$ into $\mathbb{R}^2$ in a way that is continuous and a piecewise isometry exactly on…
The aim of this research is a practical method to draw cable plans of complex machines. Such plans consist of electronic components and cables connecting specific ports of the components. Since the machines are configured for each client…
We investigate spectral properties of periodic quantum graphs in the form of a kagome or a triangular lattice in the situation when the condition matching the wave functions at the lattice vertices is chosen of a particular form violating…